[seqfan] Re: A greedy sequence
franktaw at netscape.net
franktaw at netscape.net
Sun Feb 15 00:43:31 CET 2009
I think you may have misread the reference you gave. The greedy
algorithm
for unit fractions always terminates (for a positive, rational target).
It is only
the *odd* greedy algorithm (constraining all denominators to be odd)
for
which termination is an unsolved problem. So there is no question that
all
sub-sequences do, in fact, terminate.
You need to do this kind of computation using exact, "unlimited"
precision
integer arithmetic. Any floating point arithmetic will soon fail with
this
algorithm.
Franklin T. Adams-Watters
-----Original Message-----
From: Jeremy Gardiner <jeremy.gardiner at btinternet.com>
The following 'greedy' sequence is formed by summing unit fractions
until
the sum is 1, and repeating using up the 'left over' fractions:
1,
2,3,6,
4,5,7,8,9,10,15,230,57960,
11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,1544,8242614,
31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,5
5,5
6,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80
,81
,82,202,60402,
(according to my BASIC program implementation: could be errors due to
accuracy of representation)
- anyone else find this interesting, or seen this before?
Likely needs some more investigation before thinking about submitting to
OEIS!
Perhaps related to the The Greedy Algorithm for Unit Fractions:
http://www.mathpages.com/home/kmath454.htm
I guess it may not be known if all of the sub-sequences terminate?
Jeremy
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